Let me build this single-page web app. It needs:

1. A spinning heptagon (7-sided polygon) that rotates 360 degrees every 5 seconds.
2. 20 numbered balls (1-20) dropping from the center.
3. Gravity and friction.
4. Ball-to-ball collision.
5. Ball-to-rotating-wall collision (realistic bounce, accounting for moving walls).
6. Each ball's spin shown via rotation of its number.

Let me implement the physics.

Heptagon vertices: 7 sides, angle between vertices = 2π/7. Rotate at ω = 2π/5 rad/s.

Ball physics:
- Gravity downward.
- Friction: air damping (linear velocity damping).
- Rotation: angular velocity for spin. Ball spin is affected by friction with walls (torque).
- Ball-to-ball collision: elastic collision with restitution.
- Ball-to-wall collision: walls are moving (rotating). Need to handle collision with moving wall.

Let me implement collision detection between balls (circle-circle) and ball vs polygon edges (circle-segment, treating segment as a moving line).

For ball vs rotating wall: The heptagon has edges. When a ball collides with an edge, the edge's velocity at the contact point is the angular velocity × radius vector. 

For realistic bounce: relative velocity at contact along normal. The wall is moving, so we compute impact relative to wall's contact point velocity. Restitution e.g. 0.7.

Let me also apply friction/torque on wall contact for spin.

Let me set up the coordinate system. Canvas sized W×H. Center at (cx, cy). Heptagon radius R.

Ball drop from center with random small initial positions/velocities.

Let me code it.

Physics step with substeps for stability.

Collision detection ball vs edge:
- Edge from point A to B (in world coords). The ball center p, radius r. Closest point on segment to p. If distance < r, collision.
- Normal n = (p - closestPoint)/dist pointing from wall to ball.
- Wall velocity at contact point: v_wall = ω_rot × (closestPoint - center) (rotational velocity). For rotation in canvas coordinates, velocity = ω × r vector. Let ω positive = clockwise or counterclockwise. Angular velocity vector points out of screen; velocity at point = ω × r. In 2D, v = (-ω * ry, ω * rx) where r = point - center.

- Relative velocity v_rel = v_ball - v_wall.
- Normal component vn = v_rel · n.
- If vn < 0 (approaching), apply impulse.
- Restitution: j = -(1+e)*vn. Impulse along n.
- Also tangential friction: tangential velocity vt = v_rel - vn*n. Apply friction impulse reducing tangential velocity, and produce torque (spin).

Ball spin: store angular velocity ω_b. In canvas, rotating the number by angle θ. Number text rotation.

Ball-to-ball collision:
- Dist between centers, if < sum of radii, push apart, elastic with restitution.
- Also could transfer spin but keep simple: maybe just keep spins.

Let me set radii ~ 15-18.

Let me keep all balls same radius for simplicity? Numbered balls could be same size. Let's use same radius R_BALL = 16.

Let me write code.

I'll use substeps per frame: dt fixed. Use requestAnimationFrame.

Let me handle gravity ~ 1200 px/s².

Air friction: linear damping velocity *= (1 - damping*dt) with damping ~0.2.

Let me code the wall update each frame: rotation angle θ = θ0 + ω*t, this ensures spinning 360 deg every 5s regardless of fps.

Let me geometry for heptagon vertex i: angle_i = θ + i*2π/7. Vertex coords = center + R*(cos, sin).

Edges between consecutive vertices.

Ball-wall collision loop over all edges.

Let me implement helper functions.

For closest point on segment:
```
function closestPointOnSegment(p, a, b){
  const abx=b.x-a.x, aby=b.y-a.y;
  const apx=p.x-a.x, apy=p.y-a.y;
  const len2=abx*abx+aby*aby;
  let t=(apx*abx+apy*aby)/len2;
  t=Math.max(0,Math.min(1,t));
  return {x:a.x+abx*t, y:a.y+aby*t};
}
```

Collision solve:
```
for each edge:
  cp = closestPointOnSegment(p, a, b)
  dx=p.x-cp.x, dy=p.y-cp.y
  d=hypot
  if d < r and d>0:
     n = (dx/d, dy/d)
     // wall velocity at contact point
     rx=cp.x-cx, ry=cp.y-cy
     vwx = -omega*wall*r? 
```

Wait omega in rad/s. Velocity = ω (scalar) applied as rotation. If rotation angle θ increases with time (counterclockwise in standard math, but canvas y-axis flips). Let's just compute wall point velocity as derivative of vertex positions.

Position of point at world orientation... Actually the wall point cp moves. The velocity of a point on a rotating rigid body about center: v = ω_cross × r. With angular velocity vector ω_vec = (0,0,ω). v = ω_vec × r = (-ω*ry, ω*rx) in 2D where r=(rx,ry). 

If θ(t) = ω t and rotation is counterclockwise in math coordinates, the derivative of position r(t) = (R cos(θ+φ), R sin(θ+φ)) is dv/dt = ω R (-sin, cos) = ω*(-ry, rx). Yes matches.

In canvas, that's fine—it's just physics of points moving with the vertex.

For impulse with moving wall:
- vrel = v_ball - v_wall
- vn = vrel·n
- if vn < 0: 
   - restitution e: sep velocity = -e*vn. Change in normal velocity = -(1+e)*vn.
   - impulse magnitude j = -(1+e)*vn (mass normalizing).
   - Apply Δv_ball = j*n.
- Friction: tangential. vt = vrel - vn*n. Apply friction impulse μ * |j_normal| in tangent direction opposing vt. This gives tangential velocity change and torque.

Let me include spin. Torque from friction: Δω = (tangential impulse * r) / I where I = (2/5)m r². For simplicity use moment relationship. Actually the tangential force creates torque τ = F_t * r. Δω = τ dt... but we're doing impulse-based. Tangential impulse J_t applied at point on surface. Angular impulse = J_t * r. Δω = (J_t * r)/I = (J_t * r)/((2/5) m r²) = (J_t)/( (2/5) m r). 

Hmm, this complicates. Let me keep simpler spinning model: On wall contact, add spin proportional to tangential sliding. Track angular velocity ω_b. The number rotates by θ_b += ω_b dt.

Let me implement: on collision, compute tangential impulse and update ω_b and also linear velocity.

Actually simplest visually: each ball has angular velocity. On wall collision, the tangential contact causes ball to roll — set spin based on relative tangential velocity: ω_b = -vt/r * factor. Let me just apply impulse-based spin.

Let me use a simplified sphere model:
- mass m (unit).
- I for solid sphere = 2/5 m r².
- Friction impulse Jt bounded by μ*|Jn| (μ ~0.3).
- Δv tangential = Jt/m (opposing vt).
- Δω = -(Jt * r)/I_norm... 

Let me just compute: 
vt magnitude. Apply friction to reduce vt by up to μ*|Jn|.
Δv_t = min(μ*|Jn|, |vt|) * direction.
Then tangential velocity -= Δv_t.
Spin: Δω = -Δv_t / r (rolling: contact point velocity relative to ball is vt + ω*r; perfect rolling when vt + ω_b*r = 0). Hmm.

Let me keep it physically plausible: after impulse, tangential surface velocity of ball at contact point = v_t_ball_surface = v_t_lin - ω_b * r (in the tangent direction). Rolling condition makes this zero relative to wall moving tangentially (which is ~0 for rotation, well wall tangential velocity at contact point due to rotation is nonzero).

This is getting complex. Let me simplify but keep it looking good:
- On wall contact, after computing collision, compute the ball's tangential velocity at contact: v_surf = vt (linear tangential) . Friction changes it.
- Set ω_b so that the number spins; I'll integrate ω_b from friction.

I'll implement with reasonable numbers and it'll look fine even if not perfectly physically exact. The key requirement: "show each ball's spin via the rotation of its number" and "bounce realistically off the rotating walls." 

Let me implement spin as follows:
- Ball has omega (scalar angular velocity) and angle (rotation).
- During free motion, omega decays a bit (rolling resistance) but keep mostly.
- On ball-ball and wall collisions, omega gets updated due to friction; also small random.

Actually simplest and reliable for visual "spin": when a ball collides with a wall, the friction causes the ball to spin. Set omega relative to tangential velocity: omega = -vt / r (rolling without slipping on wall). And ball-ball collisions transfer spin partially. And always integrate angle += omega*dt.

Let me just do:
- In wall collision, after solving normal, compute tangential velocity vt. Update omega: omega = clamp based. Let's set omega = -v_t/r where v_t is relative tangential velocity between ball surface and wall. Then show rolling. But v_t relates to the point's motion.

I'll compute the ball's surface tangential velocity relative to wall at contact point:
v_t_rel = v_ball_t - v_wall_t - omega * r  ... define tangential coordinate where contact point on ball surface moves at -omega*r relative to ball center? Let me define: number rotation omega positive = clockwise. The surface point at contact... 

I'll keep it simpler and physically-inspired but not over-engineered: 
- Compute relative tangential velocity at contact: relT = (v_ball - v_wall)·t_dir where t_dir is tangent unit = (n.y, -n.x) (perpendicular to n).
- The surface relative slip = relT - omega*r (assume rolling offset). Actually slip = relT + (surface speed of ball at contact). Ball surface speed at contact point = omega * r (tangential). Sign depends. Let me just do slip = relT; rolling corresponds to omega = -relT/r roughly but ignoring signs.

I think over-thinking. Let me make spin primarily driven by friction impulse during collision, giving omega the same "roll" feel, and it's fine.

Plan for wall collision function:
```
function collideWall(ball){
  for edges:
    cp = closest
    dx=ball.x-cp.x, dy=ball.y-cp.y
    d=hypot
    if(d < ball.r && d>1e-6){
      nx=dx/d, ny=dy/d
      // wall velocity at cp
      rx=cp.x-cx, ry=cp.y-cy
      vwx=-omega*ry, vwy=omega*rx
      // ball velocity
      vx=ball.vx, vy=ball.vy
      relx=vx-vwx, rely=vy-vwy
      vn=relx*nx+rely*ny
      if(vn<0){
        // push out
        ball.x=cp.x+nx*ball.r
        ball.y=cp.y+ny*ball.r
        // normal impulse with restitution
        const e=0.75
        const jn=-(1+e)*vn
        ball.vx+=jn*nx
        ball.vy+=jn*ny
        // tangent
        tx=-ny, ty=nx  // one tangent direction
        const relT=relx*tx+rely*ty
        const mu=0.3
        // max friction
        const maxF=mu*Math.abs(jn)
        let jt = -relT  // target to kill tangential
        if(Math.abs(jt)>maxF) jt=Math.sign(jt)*maxF
        ball.vx+=jt*tx
        ball.vy+=jt*ty
        // spin change: rolling feel
        // new tangential rel velocity
        ball.omega += jt/ball.r   // hmm sign
      }
      // also friction torque even without normal approach? skip
    }
}
```

Hmm the omega update sign. Let me define: omega = angular rate (rad/s), positive clockwise in canvas (y down). The tangential motion of ball surface at the contact point relative to center equals... For a ball rotating clockwise (omega>0), top surface moves left, bottom moves right. Contact point is at cp direction; tangent direction tx=-ny,ty=nx. This is geometry dependent. Hard to get exact sign.

Given visual requirement, let me make the ball spin based on actual tangential relative velocity: when ball slides along wall with tangential velocity relT, friction makes it roll. Rolling angular velocity omega_roll such that surface velocity at contact = tangential velocity of contact point relative to center. Let me just set omega to reflect sliding: 

I'll set omega = -relT / ball.r after friction (rolling condition). But if I set exactly, friction then zero... It's a compromise. Let me apply: after tangential impulse, compute new tangential rel velocity newRelT = relT + jt (since jt added to ball.v along t, reduces... relT decreases by jt because relT positive component). Then set omega via rolling: omega = -newRelT / r. 

But the exact sign between omega and relT depends on tangent orientation relative to contact geometry. Since tx,ty chosen as -ny,nx (one perpendicular), the sign mapping... Let me define properly: tangent t = (tx,ty). Contact point from center: d = (nx*ball.r, ny*ball.r). The velocity of the surface point on the ball at the contact due to rotation: cross(omega_vec, d). With omega_vec=(0,0,omega_z), cross = (-omega_z*dy, omega_z*dx) = (-omega_z*ny*r, omega_z*nx*r) = omega_z*r*( -ny, nx) = omega_z*r*(tx,ty) = omega_z*r*t. 

So surface point velocity in tangent direction = omega_z * r (projection onto t: (omega_z*r*t)·t = omega_z*r). Good. 

Total tangential relative velocity including surface: slip = relT_linear + omega_z*r? Where relT_linear is the linear relative velocity of ball center minus wall along t. The contact point of ball surface relative to wall along t = relT_linear - (surface point velocity along t) ... hmm.

Let me define slip = relative velocity of the wall-side surface point of the ball w.r.t. wall along t. Wall velocity along t: v_wall_t. Ball center along t: v_ball_t + surface offset. Surface point at contact has velocity = v_ball (center) + omega_z*r*t. 

slip = (v_ball + omega_z r t - v_wall)·t = relT_linear + omega_z*r*t·t = relT_linear + omega_z*r.

Rolling without slip: slip=0 => omega_z = -relT_linear/r. 

So the rolling angular velocity = -relT_linear/r. That's clean! So after we adjust linear tangential velocity via friction (reducing |relT|), set omega = -newRelT/r.

But we also want inertia—the ball shouldn't instantly reach rolling. But impulse-based friction already killed most tangential relative motion. Then setting omega = -newRelTL/r is consistent. However newRelT after friction might be small, giving near-zero spin. That doesn't "show spin" much.

Hmm. But friction kills slip, so the ball rolls, number rotates as it rolls along wall — that shows spin nicely. The rolling continues and number rotates as long as it moves along wall (repeated collisions). Good, that's realistic.

But I think for visual appeal "show each ball's spin via rotation of number" means balls should visibly spin. Rolling on walls gives that. Also during free fall balls have initial spin. Let me give each ball a random initial spin too.

Let me also handle friction during free rotation slightly damping omega.

Also ball-ball collisions: transfer spin a bit. On collision, the two balls' contact friction. Let me apply: after normal impulse, compute tangential relative velocity, apply friction, update both omegas using rolling differential. I'll implement ball-ball with friction too.

This is getting long but let me just write it.

Ball-ball collision:
```
function collideBallBall(a,b){
  dx=b.x-a.x, dy=b.y-a.y
  d=Math.hypot(dx,dy)
  const minD=a.r+b.r
  if(d>=minD) return
  if(d==0){dx=1;dy=0;d=1}
  nx=dx/d, ny=dy/d
  // separate
  const overlap=minD-d
  a.x-=nx*overlap/2; a.y-=ny*overlap/2
  b.x+=nx*overlap/2; b.y+=ny*overlap/2
  // relative velocity
  rvx=a.vx-b.vx, rvy=a.vy-b.vy
  vn=rvx*nx+rvy*ny
  if(vn>0){ // separating, no impulse... wait sign
     // a moving toward b: rv = a-b along n (b-a direction). contact normal is from a to b = (nx,ny). vn>0 means approaching.
     const e=0.8
     const j=-(1+e)*vn/2  // divide by 2 for equal mass impulse... actually impulse applied to a: -j? Let me just apply half.
     a.vx-=j*nx; a.vy-=j*ny
     b.vx+=j*nx; b.vy+=j*ny
     // friction / spin transfer (keep simple)
     tx=-ny,ty=nx
     const relT=a.vx*tx+a.vy*ty - (b.vx*tx+b.vy*ty)
     // rolling coupling
     const contactVOmg = ... 
  }
}
```

Let me keep ball-ball spin minimal: set omega_d if omegas differ significantly? I'll just transfer a bit: average them toward each other on strong contact. Actually to show spin, I'll do full rolling coupling which is complex. Let me do simpler partial spin exchange: 
```
a.omega += (b.omega-a.omega)*0.5*contactFactor
b.omega += (a.omega-b.omega)*0.5*contactFactor
```
where contactFactor proportionate to overlap/strength. Fine.

Actually for the requirement, wall-induced rolling spin is the main show. Let me make that robust and add initial random spins and a slight spin from air? No, spin from friction only + initial.

Let me let ball-ball tangential friction also do rolling coupling to be nicer, but keep it manageable.

I'll implement a reasonably physical rolling coupling:
On ball-ball contact, treat instantaneous. This is complex; I'll do simple spin impulse.

Given the visual goal, let me keep ball-ball collisions elastic (restitution) with slight spin exchange, and wall collisions do the rolling spin. That satisfies requirements.

Let me now write the full HTML.

Canvas size: fill window. Center heptagon. Let me respond to resize.

Simulation:
- gravity g=1500 px/s²
- dt fixed: accumulate real time, substep maybe.

Let me use rAF with dt = min(frame, 0.033). Account for wall rotation continuously: theta += omega_wall * dt where omega_wall = 2π/5.

Multiple physics substeps per frame for stability: steps = Math.ceil(dt/0.004) maybe. Let me use substep dt_st = 0.004? That's 250 steps/sec, fine.

Actually with balls possibly many collisions, let me run say 4-8 substeps per frame with dt_st = dt/steps, min dt_st 0.002.

Let me code rotation of number: ctx.save, translate to ball center, rotate by ball.angle, then also we need the ball's current angular... just draw number rotated by ball.angle. The "spin via rotation of number" = ball.angle changes over time as ball.omega changes. Good.

Draw heptagon: filled dark with border, rotating. Draw with slight fill so balls visible.

Balls start dropping from center. Spawn all at center with random small offsets and velocities, staggered? They drop from center as stated. Let me spawn them at center with small random horizontal offset and let gravity separate them. Maybe stagger spawn over time for nice visual (drop one at a time every 0.1s). The prompt says "20 numbered balls dropping from the center". I'll spawn all at center initially; or stagger. I'll stagger spawn at center + small random velocities so they cascade. Let me spawn them gradually at start (first ~2s) — all dropped from center. That looks dynamic. But then initial state has fewer. Fine.

Actually simpler: spawn all at once at center with random tangential velocities so they spread. Good enough and clearly "dropping from center". I'll add slight time staggering (0.05s apart) using a spawn list with delays.

Let me implement spawn queue: for i, spawnDelay = i*0.08. Balls not yet spawned are pending. Each frame spawn due ones at center (with tiny random velocity/spin).

Wall rotation: if wall spins 360 deg every 5s, omega_wall=2π/5≈1.257 rad/s. That's slow-ish. Balls inside will gently be carried. Balls spawning at center — center is inside, no initial wall collision until they reach edges. Fine.

Let me set heptagon radius large enough relative to canvas: min(W,H)*0.35.

Let me write the code now.

Edge cases: balls may escape through vertices/gaps? Should be fine with close point on segment. Balls could tunnel if moving too fast relative to thin walls. Substeps + pushing out on the correct side. Our wall collision detects overlap regardless of side (using closest point, d<r), pushes out along normal, and applies restitution if approaching. Good, robust. But could a ball get pushed to wrong side? If ball passes fully through edge in one substep, could end beyond. With substeps and speed limits probably ok. Let me also add a speed cap maybe. Keep substep small.

Let me finalize numbers:
- Heptagon radius: R = 0.38 * min(cw,ch)
- Ball radius r=15
- gravity g=1700
- restitution wall e=0.72, ball e=0.82
- friction mu=0.20
- air damping: vx*=Math.max(0,1-0.6*dt)? Let me apply linear damp ~ light. Let me set: vx -= vx*0.08*dt? I'll use drag: multiply by (1 - drag*dt) with drag=0.15.

Actually with friction on walls, air damping low.

Let me now write everything.

For the number rendering, draw a filled inner circle and number on top, both rotated.

Let me code the draw of ball:
```
ctx.save()
ctx.translate(ball.x, ball.y)
ctx.rotate(ball.angle)
// circle
ctx.beginPath(); ctx.arc(0,0,ball.r,0,2π); fill color; stroke
// number
ctx.fillText(String(ball.num), 0, 4)
ctx.restore()
```
Number centered: use textAlign center, baseline middle.

Ball angle increases by ball.omega*dt.

Color per number: gradient by number. Use HSL.

Let me write final file.

Let me also add a HUD title text maybe. Sure, small label.

Let me write it.

Let me carefully write the physics update loop.

```
let cx, cy, HEG_R;
let wallOmega = 2*Math.PI/5;
let wallAngle = 0;

function updatePhysics(dt){
  // wall angle
  wallAngle += wallOmega*dt;
  // spawn pending
  ...
  // step balls
  const steps = 5; // fixed-ish
  const sub = dt/steps;
  for(let s=0;s<steps;s++){
    for(const b of balls){
      // gravity
      b.vy += GRAV*sub;
      // drag
      b.vx *= (1-DRAG*sub);
      b.vy *= (1-DRAG*sub);
      b.x += b.vx*sub;
      b.y += b.vy*sub;
      // spin decay
      b.omega *= (1-0.5*sub); // mild
      b.angle += b.omega*sub;
      cull if outside
      // wall collision
      if(DO_WALL) collideWalls(b, sub);
    }
    // ball-ball
    for(let i=0;i<balls.length;i++)for(let j=i+1;j<balls.length;j++) collideBallBall(balls[i],balls[j]);
  }
}
```

Static walls flag to disable. I'll add key 'w' to toggle gravity? Not needed. Keep gravity always.

Let me implement collideWalls with the geometry recomputed inside or precomputed. Precompute vertices each frame (angle changes). Pass to function.

Let me compute vertices in update based on wallAngle, store in array for drawing too.

```
function heptagonVertices(){
  const vs=[];
  for(let i=0;i<7;i++){
    const a=wallAngle + i*2*Math.PI/7;
    vs.push({x:cx+HEG_R*Math.cos(a), y:cy+HEG_R*Math.sin(a)});
  }
  return vs;
}
```

Wall collision:
```
function collideWalls(b, vs){
  for(let i=0;i<7;i++){
    const A=vs[i], B=vs[(i+1)%7];
    // normal pointing outward: use cross product
    const cp = closestPointOnSegment(b, A, B);
    let dx=b.x-cp.x, dy=b.y-cp.y;
    let d=Math.hypot(dx,dy);
    if(d>=b.r) continue;
    let nx,ny;
    if(d>1e-6){ nx=dx/d; ny=dy/d; }
    else {
      // center on segment; use outward normal
      const ex=B.x-A.x, ey=B.y-A.y;
      const el=Math.hypot(ex,ey); 
      // outward normal
      nx = ey/el; ny = -ex/el;
      // need outward: check which side center of polygon is
      // polygon center (cx,cy). dot((mid-cx),n) should be positive for outward
      const mx=(A.x+B.x)/2, my=(A.y+B.y)/2;
      if((mx-cx)*nx+(my-cy)*ny < 0){ nx=-nx; ny=-ny; }
    }
    // reposition
    b.x = cp.x + nx*b.r;
    b.y = cp.y + ny*b.r;
    // wall velocity at cp
    const rx=cp.x-cx, ry=cp.y-cy;
    const vwx = -wallOmega*ry, vwy = wallOmega*rx;
    const relx=b.vx-vwx, rely=b.vy-vwy;
    const vn = relx*nx + rely*ny;
    if(vn<0){
      const e=0.72;
      const jn=-(1+e)*vn;
      b.vx += jn*nx; b.vy += jn*ny;
      // tangent
      let tx=-ny, ty=nx;
      const relT = relx*tx + rely*ty;
      const mu=0.25;
      const maxF = mu*Math.abs(jn);
      let jt=-relT;
      if(Math.abs(jt)>maxF) jt=Math.sign(jt)*maxF;
      b.vx += jt*tx; b.vy += jt*ty;
      // rolling spin set
      const newRelT = relT + jt; // linear tangential rel reduced
      // omega_roll = -newRelT / r
      // blend fast
      const targetOmg = -newRelT/b.r;
      b.omega = targetOmg;
    }
  }
}
```

Setting b.omega = targetOmg is a strong coupling (friction strong enough to force rolling). That's fine and shows spin. But it kills sliding quickly—realistic sticky. mu small would limit, but I set omega directly regardless. Let me instead set omega with blend: b.omega = b.omega*0.3 + target*0.7, to feel like inertia. Actually since we already reduced tangential velocity by friction jt, target fits. Let me set b.omega = target. But if |jt| was capped by maxF, then newRelT isn't zero, target non-zero consistent. Fine, set b.omega=target.

Wait jt sign: we add jt*t to b.v where jt=-relT. So b.v_t changes by -relT, killing tangential relative motion (newRelT=0) when not capped. Then target=0 => omega=0. That means no spin after sliding stops?? Hmm that contradicts. Let me reconsider.

When ball hits wall with tangential motion relT, friction reduces linear tangential velocity to match wall. For rolling, ball should spin with omega=-newRelT/r but newRelT→0. So ball ends up not spinning relative to wall — it stops sliding and doesn't roll because it also stopped moving tangentially (stuck to wall quickly). Not great for showing spin.

But realistically, when ball slides and friction acts purely tangentially removing linear slip, the resulting motion is non-slip sliding (no rotation), which is not rolling. True contact mechanics include tangential force AND torque simultaneously; rolling emerges when the tangential linear velocity isn't fully killed but converted to rotation.

To show nice rolling spin, let me use a proper rolling coupling on contact: friction converts linear tangential motion into rotation (rolling). Model: at contact, if slip, apply friction that reduces slip = relT_linear + omega*r and produces both Δv and Δω.

slip = relT + omega*r (from earlier derivation where omega is ball's scalar with t convention).

Friction acts to reduce |slip|. If we eliminate slip: target relT + omega*r = 0.

Impulse Jt applied along +t to offset... And angular: Δω = (Jt * r)/(I) where for solid sphere I=2/5 m r², Δω = Jt*r/I = Jt*r/((2/5)m r²)= Jt*(5)/(2 m r). With m=1: Δω=5 Jt/(2 r).

And linear Δv_t = Jt (for ball, m=1).

The friction impulse direction opposes slip.

Let me solve: we want after impulse, slip'=0 (sticking friction if possible, bound by Coulomb limit).
slip' = (relT + Jt) + (omega + Δω)*r = relT + omega*r + Jt + Δω*r.
Δω*r = Jt*5/(2 r)*r = Jt*2.5.
So slip' = relT + omega*r + Jt*(1+2.5)= relT+omega*r + 3.5 Jt.
Set slip'=0 => Jt = -(relT+omega*r)/3.5.
Bound |Jt| <= mu*|Jn|.

This models genuine rolling from sliding with inertia. 

Let me implement this for wall contact. On wall contact:
- resolve normal impulse jn (this changes vn).
- compute relT linear and existing omega.
- slip = relT + omega*r.
- Jt = -slip/3.5, clamp to ±mu*|jn|.
- b.vx += Jt*tx; b.vy += Jt*ty;
- b.omega += 2.5*Jt/(r);  (since Δω = 5 Jt/(2r) = 2.5 Jt/r)
Wait Δω = Jt*5/(2 r) = 2.5*Jt/r. Yes.

But sign of t relative to omega — I derived omega*r * t projection giving slip = relT + omega*r with the t convention where surface point velocity = omega*r*t. But note: surface point velocity = omega_z*r*t. Projection onto t = omega_z*r (since t·t=1). But is omega positive meaning clockwise? The relation cross(omega_vec, d)=omega_z r t gives surface velocity in direction t equal omega_z r. So slip along t = relT + omega_z r. Good, with omega measured as "omega_z" where rotation by angle θ in canvas. Canvas rotation positive = clockwise visually. Our vertex rotation positive also = clockwise (as angle increases, x=cos, y=sin in canvas gives clockwise). Consistent.

But careful: tangent t=-ny,nx is one of two directions; we chose it arbitrarily. The slip formula uses t; omega*z*r along t corresponds to surface velocity along t. Since both use same t, consistent. Good.

Now omega decays and integrates. Good.

Let me also add: when wall moving (vw), relT computed relative to wall. Good, already using rel vector from wall.

Alright let me also do ball-ball with proper rolling coupling similarly but symmetrical. That's more complex (two bodies). Let me do a simpler elastic collision with partial spin. For ball-ball, I'll implement:

Normal impulse jn. Then tangential friction symmetric: slip = relative tangential velocity of the two surfaces at contact. Surface velocities: for ball a at contact point (in direction from a to b, i.e., normal n), surface point velocity due to spin = omega_a r ×? Similar derivation. Contact normal n points a→b. Contact point on a at a+n*r. Cross(omega_a_vec, n*r) = omega_a*r*(-n? )... Let me just use approximate: slip = (v_a - v_b)·t + (omega_a + omega_b)*r? This is getting messy. Given added complexity, for ball-ball I'll do: elastic normal collision + mild friction on linear tangential velocity + small spin impulse exchange. The visual is dominated by wall rolling anyway.

Ball-ball:
```
function collideBallBall(a,b){
  let dx=b.x-a.x, dy=b.y-a.y;
  let d=Math.hypot(dx,dy);
  const minD=a.r+b.r;
  if(d>=minD) return;
  if(d<1e-6){dx=0.01;dy=-1;d=Math.hypot(dx,dy);}
  const nx=dx/d, ny=dy/d;
  const overlap=minD-d;
  a.x-=nx*overlap/2; a.y-=ny*overlap/2;
  b.x+=nx*overlap/2; b.y+=ny*overlap/2;
  const rvx=a.vx-b.vx, rvy=a.vy-b.vy;
  const vn=rvx*nx+rvy*ny;
  if(vn>0){
    const e=0.8;
    const j=-(1+e)*vn/2; // equal mass
    a.vx-=j*nx; a.vy-=j*ny;
    b.vx+=j*nx; b.vy+=j*ny;
    // spin exchange / friction
    const tx=-ny, ty=nx;
    const relT=rVx... // relative tangential of centers
    const relT=(a.vx-b.vx)*tx+(a.vy-b.vy)*ty;
    const mu=0.15;
    const maxF=mu*Math.abs(j);
    let f=-relT/2;
    if(Math.abs(f)>maxF) f=Math.sign(f)*maxF;
    a.vx+=f*tx;a.vy+=f*ty;
    b.vx-=f*tx;b.vy-=f*ty;
    // spin impulse: rolling coupling approximate
    a.omega += (f*2.5/a.r)*0.5;
    b.omega -= (f*2.5/b.r)*0.5;
  } else {
    // not approaching but overlapping; maybe just push but no impulse. push already done.
  }
}
```

The spin coupling signs approximate. It's fine for visuals.

Now spawn logic. Let me create balls array. Ball object: {num,x,y,vx,vy,r,angle,omega,color}.

Spawn queue: delays[i]=i*0.1. Track elapsed time. Spawn when elapsed>=delay. At spawn set position = center + small random offset (say ±8), velocity small random (or from just below center). Spin initial random small.

Let me also make balls spawn with a tiny downward push. They'll drop from center.

Alright, drawing heptagon: fill with semi-dark gradient, stroke bright. Since it rotates, compute fill path.

Draw background: dark.

Add subtle glow. Keep simple.

Let me also draw center marker maybe.

Let me finalize and write file. Also handle window resize to recenter but keep ball positions? On resize, update cx,cy,HEG_R. Balls outside new polygon just get caught by walls. Fine.

Let me write index.html.

Let me make numbers clearly visible: white number on colored ball with dark border.

Choose ball colors by number: hue = 210 - (num-1)*(240/19)? Or palette. Use hsl(((num*37)%360),70%,55%). Random-looking distinct.

Let me write.

Speed cap: to prevent tunneling, cap speed at like 40*? Let me cap v to 3000 in substep movement. Actually wall collision push-out handles full tunneling too because it checks d<r and pushes along normal outward; if ball went past boundary, closest point still on edge, normal may point inward instead of outward though. My normal uses outward direction based on polygon center test only when d tiny. For the general d>0 case, nx,ny = (ball - cp) direction which points from wall point into ball — if ball is outside polygon, that's outward; if ball somehow inside beyond edge, that direction points inward, pushing it wrong way (deeper). To be safe, ensure n points outward: compute outward candidate and compare dot with (ball-cp) direction; if they oppose (dot<0), flip. That guarantees push outward relative to polygon interior.

Let me add: compute outward normal of edge. Then n = direction(ball-cp) but ensure it points outward: if dot(n_out, n_candidate)<0, flip.

Let me define outward normal using cross product. For vertex i,a and a+1,b: outward = perpendicular of edge pointing away from polygon center. e=(ex,ey), normal candidates (ey,-ex) and (-ey,ex). Pick one pointing away from center: dot(normal, (midpoint - center))>0.

Let me precompute outward normals for edges each frame along with vertices.

I'll incorporate.

Alright, write the file now.

Let me also add a slight max speed for stability: after impulse if speed>some max clamp. Keep.

Let me code spawn with slight stagger and production.

Let me write the complete file.

Let me set DRAG small like 0.05 so balls keep momentum. Actually requirement says "friction" — we have wall friction and some air drag. Fine.

I'll write now.

Let me assemble the JS carefully in one script tag.

Canvas sizing full window. Use devicePixelRatio for crispness.
```
function resize(){
  const dpr=window.devicePixelRatio||1;
  const w=innerWidth,h=innerHeight;
  canvas.width=w*dpr; canvas.height=h*dpr;
  canvas.style.width=w+'px'; canvas.style.height=h+'px';
  ctx.setTransform(dpr,0,0,dpr,0,0);
  cw=w; ch=h;
  cx=w/2; cy=h/2;
  HEG_R=Math.min(cw,ch)*0.38;
}
```

Good.

Let me store radius maybe vary ball sizes randomly 12-17 for richer collisions? Requirement says numbered balls; uniform maybe cleaner but varied is fine. I'll keep uniform 15 for predictable.

Let me finalize gravity so balls reach walls. Walls big, gravity 1500. Fine.

Let me write it.

I'll ensure first spawn happens at t=0 (delay 0), then stagger 0.12s each. 20 balls, last at ~2.3s. Smooth.

Let me include a status line showing time and spins? Optional. I'll add small title overlay.

Now writing.

Empty workspace. Let me write the file.

Let me verify the file is syntactically valid via node. Let me extract the script and check for JS syntax errors.

The file is valid. Let me double check the collisionDirection / wall angle spawn logic — pendingStart and time relationship. On initSpawn, time keeps, but spawnQueue delays are relative starting from pendingStart=time. Its fine.

Wait, `initSpawn()` sets balls=[], spawnQueue with delays relative 0. But spawn condition `spawnQueue[0].delay <= time - pendingStart`. After initSpawn, pendingStart=time, so time-pendingStart=0, first delay 0 spawns immediately, others stagger. Good. On R key, reset. Good.

One issue: on refresh via R, pendingStart set to time, fine.

Let me quickly sanity-check a couple of physics things conceptually. The wall collision normal guarantee: I compute nx,ny from ball-cp, then verify outward vs midpoint-center. Good.

Let me consider the ball-ball spinning approximation uses b.r for both `slip` and omega of b — approximate, fine.

The spawn: first ball delay=0 spawns immediately on first step. Good.

Potential issue: In the main loop, wallAngle and buildWall called in stepPhysics; frame calls draw which rebuilds wall too. Fine.

I think this is complete. Let me verify it opens — can't run browser here but syntax is valid.

Let me finalize.